Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks (2020-08-13T00:00:00.000000Z)

TL;DR

This work presents a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems, based on deep neural networks.

Authors

K. Lye

2 papers

Siddhartha Mishra

2 papers

Deep Ray

2 papers

P. Chandrasekhar

1 papers

TL;DR

Authors

References56 items

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ETH Z¨urich, R¨amistrasse 101, Z¨urich-8092, Switzerland ‡ Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, U.S.A § TIFR

Draw 𝑁 random starting points ˜ 𝑦 1

Step The following remarks about algorithm

Goal Compute (approximate) minimizers for the PDE constrained optimization problem (2.4)

Inputs Parametrized PDE (2.1) , observable (2.2) , cost function (2.5) , training set S ⊂ 𝑌 (either randomly chosen or suitable quadrature points such as low discrepancy sequences)

For an initial value of the weight vector 𝜃 ∈ Θ , evaluate the neural network L 𝜃 (2.9) , the loss function (2.15) and its gradients to initialize the (stochastic) gradient descent algorithm

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